A century is any 100 year period, however the accepted  calendar century of today was instituted in 1582 by Pope Gregory XIII.  Known as the Gregorian calendar, his confirmation of 'Anno Domini' cites Jesus' life as the basis of our calendar time.  Pope Gregory XIII 'bull' (document) defined our modern definition of a century from the birth of Jesus as year 1, however the years 1 to 100 were recognized as the time of Jesus, while the following years beginning with the year 101 were recognized as the years after Jesus. 'Anno Domini' translated is 'In the year of our Lord' (meaning after the Jesus' time on earth) this is why 2009 is the 21st century.

Just an F.Y.I.- The influence of the Roman Empire was and still can be found everywhere. In this case the history of the  word 'century' could be traced to the ancient Roman 'centurion'. A Roman officer in charge of a 'century' originally made up of 100 men.

A century is defined as a 100 year period.  Currently, we are in the 21st century, meaning we are in the years beginning with 2000.  It is a bit confusing in terms of understanding the relationship between years and century.  Reflecting on it, thought, it makes sense. The years we are in is always one behind the century number.  This is because it takes 100 years to mark a century.  For example, the 19th century is considered the 1800s, because it is one behind the century number.  The 16th century covers the 1500s.  This same logic is why we are in the 21st century.